Final answer:
The direction angle of the vector (-2,5) is approximately 111.8°. It is found by taking the arctan of the ratio of its y-component to its x-component, and then adjusting for the fact that the vector is in the second quadrant by adding 180°.
Step-by-step explanation:
To find the direction angle of the vector (-2,5), we can use the tangent function, which relates the y-component to the x-component of the vector. The direction angle, often denoted as θ, is the angle measured counterclockwise from the positive x-axis to the vector. For the vector (-2,5), the tangent of the angle is the y-value divided by the x-value, which results in a negative value because the vector is in the second quadrant. Therefore, we use the following process:
- Find the arctan (inverse tangent) of the ratio of the y-component to the x-component. In this case, arctan(5/(-2)).
- Since the calculator will give us an angle in the fourth quadrant, we need to add 180° to get the angle in the second quadrant, because angles are defined as positive in the counterclockwise direction.
θ = arctan(5/(-2)) + 180°
When we calculate arctan(5/(-2)), we get an angle of approximately -68.2°. Since we're in the second quadrant, we need to add 180°:
θ = -68.2° + 180° = 111.8°
Therefore, the direction angle of the vector (-2,5) is approximately 111.8°.